Answer :
To find out how many dresses are in Amina's wardrobe, we can follow these steps:
1. Identify the given ratio: We are given that the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex]. This means for every 7 T-shirts, there are 6 dresses.
2. Identify the number of T-shirts: We know there are 28 T-shirts in her wardrobe.
3. Set up a proportion: Since the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex], we can set up a proportion to find the number of dresses. Let's denote the number of dresses by [tex]\( D \)[/tex].
The proportion can be written as:
[tex]\[ \frac{\text{Number of T-shirts}}{\text{Number of dresses}} = \frac{7}{6} \][/tex]
Substituting the number of T-shirts we have:
[tex]\[ \frac{28}{D} = \frac{7}{6} \][/tex]
4. Solve for the number of dresses (D): Now we solve for [tex]\( D \)[/tex] by cross-multiplying:
[tex]\[ 28 \times 6 = 7 \times D \][/tex]
[tex]\[ 168 = 7D \][/tex]
5. Divide both sides by 7 to isolate [tex]\( D \)[/tex]:
[tex]\[ D = \frac{168}{7} \][/tex]
[tex]\[ D = 24 \][/tex]
Thus, there are 24 dresses in Amina's wardrobe.
1. Identify the given ratio: We are given that the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex]. This means for every 7 T-shirts, there are 6 dresses.
2. Identify the number of T-shirts: We know there are 28 T-shirts in her wardrobe.
3. Set up a proportion: Since the ratio of T-shirts to dresses is [tex]\( 7:6 \)[/tex], we can set up a proportion to find the number of dresses. Let's denote the number of dresses by [tex]\( D \)[/tex].
The proportion can be written as:
[tex]\[ \frac{\text{Number of T-shirts}}{\text{Number of dresses}} = \frac{7}{6} \][/tex]
Substituting the number of T-shirts we have:
[tex]\[ \frac{28}{D} = \frac{7}{6} \][/tex]
4. Solve for the number of dresses (D): Now we solve for [tex]\( D \)[/tex] by cross-multiplying:
[tex]\[ 28 \times 6 = 7 \times D \][/tex]
[tex]\[ 168 = 7D \][/tex]
5. Divide both sides by 7 to isolate [tex]\( D \)[/tex]:
[tex]\[ D = \frac{168}{7} \][/tex]
[tex]\[ D = 24 \][/tex]
Thus, there are 24 dresses in Amina's wardrobe.
